Baldry was born in Redhill, Surrey. He and his family lived in Moscow and Warsaw until he was seven. He attended Gayhurst School while his father worked for the Cadbury company, before finally returning to England in 2003. He also speaks fluent Russian and English. In 2008, Baldry was sent back to school again to Stoke Mandeville Combined School where he participated in many Sports activities. He went on to become a Dancer, singer and theatre actor at Jackie Palmer High School. His parents are Simon and Corina Baldry.
On 28 March 2016, Baldry began appearing regularly in the Channel 4 soap opera, Hollyoaks, as Liam Donovan, one of three half brothers to established character, Grace Black, played by Tamara Wall respectively. Jimmy Essex and Luke Jerdy were later introduced as Liam's brothers, Adam and Jesse, with Grace and their mother, Tracey, with by former Loose Women panellist Lisa Maxwell, in the role.
On 10 April 2017, it was announced in the show's E4 first look episode that Liam would be leaving Hollyoaks, with Baldry making his final appearance on 11 April 2017.